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While Cauchy's equation (blue line) deviates significantly from the measured refractive indices outside of the visible region (which is shaded red), the Sellmeier equation (green dashed line) does not. The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium.
Wolfgang Sellmeier was a German theoretical physicist who made major contributions to the understanding of the interactions between light and matter. [1] In 1872 he published his seminal work Ueber die durch die Aetherschwingungen erregten Mitschwingungen der Körpertheilchen und deren Rückwirkung auf die ersteren, besonders zur Erklärung der Dispersion und ihrer Anomalien. [2]
In optics, Cauchy's transmission equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy , who originally defined it in 1830 in his article "The refraction and reflection of light".
Several laws have approximated this relationship to wavelength, notably Cauchy's law and Sellmeier equation. The refractive index of a glass is given for the yellow line known as the d line of helium (then noted n d) or for the green e line of mercury (then noted n e), depending on usage and the two main standards used. [9] [10] [11]
This alternate takes the difference between cadmium's blue (C ′) and red (F ′) refractive indices at wavelengths 480.0 nm and 643.8 nm, relative to for mercury's e line at 546.073 nm, all of which are close by, and somewhat easier to produce than the C, F, and e lines.
Forouhi-Bloomer model. The real (blue solid line) and imaginary (orange dashed line) components of complex refractive index are plotted for model with parameters = 1.3 eV, = 1.4910 eV, = 5.2139 eV, = 8.6170 eV, and = 1.5256.
A. R. Forouhi and I. Bloomer deduced dispersion equations for the refractive index, n, and extinction coefficient, k, which were published in 1986 [1] and 1988. [2] The 1986 publication relates to amorphous materials, while the 1988 publication relates to crystalline.
The real (blue solid line) and imaginary (orange dashed line) components of relative permittivity are plotted for model with parameters = 3.2 eV, = 4.5 eV, = 100 eV, = 1 eV, and = 3.5. The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity , sometimes referred to as the ...